Rellich, Gagliardo—Nirenberg, Trudinger and Caffarelli—Kohn—Nirenberg inequalities for Dunkl operators and applications

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Velicu A., Yessirkegenov N.

Israel Journal of Mathematics, vol.247, no.2, pp.741-782, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 247 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s11856-021-2261-7
  • Journal Name: Israel Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.741-782
  • Süleyman Demirel University Affiliated: No

Abstract

© 2021, The Hebrew University of Jerusalem.In this paper we introduce several extended versions of the classical Caffarelli—Kohn—Nirenberg inequalities. Moreover, we obtain weighted higher order Rellich, weighted Gagliardo—Nirenberg, Caffarelli—Kohn—Nirenberg, Trudinger inequalities and the uncertainty principle for Dunkl operators. Furthermore, we give an application of the Gagliardo—Nirenberg inequality to the Cauchy problem for the nonlinear damped wave equations for the Dunkl Laplacian.